Teacher Guide: Writing Algebraic Expressions
Learn how to translate words and real-world situations into algebraic expressions using variables and operations.
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Class quiz
10 questions on Algebraic Expressions. Students join with a name, you see everyone's score.
For Teachers
- Translate verbal phrases into algebraic expressions
- Identify key words that indicate mathematical operations
- Correctly handle 'less than' and 'more than' phrases
- Write expressions for real-world situations with one or more operations
- Use appropriate variables to represent unknown quantities
- • Understanding of basic arithmetic operations
- • Familiarity with variables as placeholders for numbers
- • Knowledge of order of operations
- 1. Can you think of a situation in your life that could be described with an algebraic expression?
- 2. Why might 'less than' be confusing? How can we remember the correct order?
- 3. If a store says '20% off,' how would you write an expression for the sale price?
- 4. What's the difference between '5 times a number plus 3' and '5 times the sum of a number and 3'?
Thinking order doesn't matter for subtraction phrases
Confusing expressions with equations
Thinking variables must be specific numbers
For Struggling Students:
- • Provide a keywords reference chart to keep on desks
- • Start with single-operation expressions before combining
- • Use manipulatives to model 'more than' and 'less than'
For On-Level Students:
- • Write expressions with two operations
- • Translate real-world scenarios into expressions
- • Identify whether given expressions match verbal descriptions
For Advanced Students:
- • Write expressions with parentheses and multiple operations
- • Create their own word problems for given expressions
- • Compare equivalent expressions (e.g., vs )
- 6.EE.A.2a (CCSS.MATH.CONTENT.6.EE.A.2.A)
Write expressions that record operations with numbers and with letters standing for numbers
- 6.EE.B.6 (CCSS.MATH.CONTENT.6.EE.B.6)
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem
- visualOperation Keywords Chart
Reference chart matching words to symbols
- activityExpression Matching Game
Match phrases to their algebraic expressions
- worksheetReal-World Expression Writing
Practice translating situations into expressions
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Definition
Key Phrases to Know
| Operation | Key Words | Example Phrase | Expression |
|---|---|---|---|
| Addition () | sum, plus, more than, increased by, total | five more than a number | |
| Subtraction () | difference, minus, less than, decreased by, fewer | a number decreased by 3 | |
| Multiplication () | product, times, of, twice, triple | twice a number | |
| Division () | quotient, divided by, ratio, per | a number divided by 4 |
- "5 more than " means
- "5 less than " means (not )
Worked Examples
Write an expression for: "The sum of a number and 12"
Identify the operation
"Sum" means addition () → Operation:
Identify the quantities
"A number" (unknown) and 12 → Variable and 12
Choose a variable
Let represent "a number" →
Write the expression
Sum means add: →
Answer:
Common Mistakes
Writing "5 less than " as instead of
Why it's wrong: "Less than" reverses the order! "5 less than " means start with and take away 5.
Correct: "5 less than " = . Think: "I have dollars and spend 5" leaves .
Forgetting to use parentheses when needed
Why it's wrong: "Twice the sum of and 3" needs parentheses to show you add first.
Correct: "Twice the sum of and 3" = , not
Confusing "a number" with a specific number
Why it's wrong: "A number" means an unknown value that should be a variable.
Correct: Always use a variable (, , ) when you see "a number," "some number," or "an unknown."
Why It Matters
- Problem Solving: Real-world problems are written in words. To solve them, you must first translate them into mathematical expressions.
- Communication: Expressions let you describe patterns and relationships concisely. Instead of saying "add 5 to whatever number you have," you write .
- Programming: Every app, game, and website uses expressions. When a game calculates your score as "base points times bonus multiplier," that's !
- Science: Formulas like distance = speed time () are algebraic expressions describing how the world works.
Real World Applications
Shopping and Budgeting
Stores use expressions to calculate totals with discounts, tax, and multiple items.
Example:
If shirts cost 15 dollars each and you have a 10 dollar coupon, the cost for shirts is .
A streaming service charges 8 dollars per month plus a one-time 20 dollar setup fee.
Write an expression for the total cost after months.
Step 1: Write the mathematical expression
Monthly cost times months plus setup fee:
Sports Statistics
Athletes and coaches use expressions to track performance and predict outcomes.
Example:
If a basketball player scores points per game, their total after games is .
A runner improves by 30 seconds each week. Their initial time was 8 minutes (480 seconds).
Write an expression for their time after weeks of training.
Step 1: Write the mathematical expression
Initial time minus improvement per week times weeks:
Cooking and Recipes
Recipes are scaled using expressions when cooking for different numbers of people.
Example:
A recipe uses 2 cups of flour per person. For people, you need cups.
A pizza recipe needs 3 cups of cheese for every 2 pizzas, plus 1 extra cup for the crust.
Write an expression for the cheese needed for pizzas (where is even).
Step 1: Write the mathematical expression
Cheese per 2 pizzas times number of pairs plus extra:
Key Takeaways
- 1Algebraic expressions translate words into math using variables and operations
- 2Key words signal operations: sum (+), difference (-), product (x), quotient (/)
- 3Watch word order carefully: "5 less than " means , not
- 4Use parentheses to group operations: "twice the sum" =
- 5Variables represent unknown or changing quantities in real situations
Frequently Asked Questions
Does it matter what letter I use for a variable?
Why is written without a multiplication sign?
How do I know when to use parentheses?
Glossary
- Algebraic expression
- A combination of numbers, variables, and operations (like )
- Variable
- A letter that represents an unknown or changing number (like , , or )
- Coefficient
- The number multiplied by a variable (in , the coefficient is 3)
- Constant
- A number without a variable (in , the constant is 5)
- Term
- A single part of an expression separated by + or - (in , the terms are and )